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BEGIN:VEVENT
SUMMARY:Optimal financing and investment strategies under asymmetric infor
mation about collateral value
DTSTART:20180830T103000Z
DTEND:20180830T110000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3137@indico.math.cnrs.fr
DESCRIPTION:Speakers: Takashi Shibata (Tokyo Metropolitan University)\n\nW
e examine the interactions between financing (capital structure) and inves
tment decisions of a firm under asymmetric information about collateral (l
iquidation) value between well-informed managers and less-informed investo
rs. We show that asymmetric information reduces the amount of debt issuanc
e to finance the cost of investment\, that leads to delay corporate invest
ment. In particular\, an increase in the degree of asymmetric information
forces the firm to be a risk-free debt-equity financing (ultimately be th
e all-equity financing) by reducing the amount of debt issuance. In additi
on\, an increase in the cash flow volatility decreases the amount of debt
issuance\, credit spread\, and leverage under asymmetric information. Our
results fit well with empirical studies. This is a joint work with Michi N
ishihara.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3137/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Fairness of Systemic Risk Measures
DTSTART:20180830T063000Z
DTEND:20180830T071000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3139@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marco Frittelli (Milano University)\n\nIn our previo
us paper\, we have introduced a general class of systemic risk measures th
at allow random allocations to individual banks before aggregation of thei
r risks. In the present paper\, we address the question of fairness of the
se allocations and we propose a fair allocation of the total risk to indiv
idual banks. We show that the dual problem of the minimization problem whi
ch identify the systemic risk measure\, provides a valuation of the random
allocations which is fair both from the point of view of the society/regu
lator and from the individual financial institutions. The case with expone
ntial utilities which allows for explicit computation is treated in detail
s.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3139/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mass-Conserving Stochastic Partial Differential Equations and Rela
ted Backward Doubly Stochastic Differential Equations
DTSTART:20180830T075000Z
DTEND:20180830T082000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3138@indico.math.cnrs.fr
DESCRIPTION:Speakers: Huaizhong Zhao (Loughborough University)\, Qi Zhang
(Fudan University)\n\nIn this talk\, i will introduce a type of mass-conse
rving stochastic partial differential equations which can be connected wit
h a type of mass-conserving backward doubly stochastic differential equati
ons. The Poincare’s inequality is used in the estimates to relax the mon
otonic condition of backward doubly stochastic differential equations.\n\n
https://indico.math.cnrs.fr/event/3123/contributions/3138/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Classical and Restricted Impulse Control for the Exchange Rate und
er Incomplete Knowledge of the Model
DTSTART:20180829T142000Z
DTEND:20180829T145000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3136@indico.math.cnrs.fr
DESCRIPTION:Speakers: Wolfgang Runggaldier (University of Padova\, Italy)\
, Kazuhiro Yasuda (Hosei University\, Tokyo\, Japan)\n\nABSTRACT: We consi
der the problem faced by a Central Bank of optimally\ncontrolling the exch
ange rate over a finite time horizon\, whereby it can use\ntwo non-excludi
ng tools: controlling directly the exchange rate in the\nform of an impuls
e control\; controlling it indirectly via the domestic\nexchange rate in t
he form of a continuously acting control. In line\nwith existing literatur
e we consider this as a mixed\nclassical-impulse control problem for which
\, on the basis of a\nquasi-variational inequality\, we search for an anal
ytic solution within a\nspecific class of value functions and controls. Be
sides the finite\nhorizon\, the main novelty here is the assumption that t
he drift in the\nexchange rate dynamics is not directly observable and has
thus to be\nfilter-estimated from observable data. The problem becomes th
us time\ninhomogeneous and the Markovian state variables have to include a
lso\nthe filter of the drift. This is a joint work with \n> Kazuhiro Yasud
a.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3136/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Entropy and additional utility of a discrete information disclosed
progressively in time
DTSTART:20180828T140000Z
DTEND:20180828T143000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3140@indico.math.cnrs.fr
DESCRIPTION:Speakers: Anna Aksamit (University of Sydney)\n\nThe additiona
l information carried by enlarged filtration and its measurement was studi
ed by several authors. Already Meyer (Sur un theoreme de J. Jacod\, 1978)
and Yor (Entropie d'une partition\, et grossissement initial d'une filtrat
ion\, 1985)\, investigated stability of martingale spaces with respect to
initial enlargement with atomic sigma-field. We extend these consideration
s to the case where information is disclosed progressively in time. We def
ine the entropy of such information and we prove that its finiteness is en
ough for stability of some martingale spaces in progressive setting. Final
ly we calculate additional logarithmic utility of a discrete information d
isclosed progressively in time.\n\nhttps://indico.math.cnrs.fr/event/3123/
contributions/3140/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Construction of an aggregate consistent utility\, without Pareto o
ptimality
DTSTART:20180829T085000Z
DTEND:20180829T092000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3141@indico.math.cnrs.fr
DESCRIPTION:Speakers: Caroline HILLAIRET (Ensae Paris tech\, CREST)\, Moha
med Mrad (University Paris 13)\, Nicole El Karoui El Karoui (LPMA)\n\nThe
aim of this talk is to describe globally the behavior and preferences of
heterogeneous agents. Our starting point is the aggregate wealth of a give
n economy\, with a given repartition of the wealth among investors\, which
is not necessarily Pareto optimal.\nWe propose a construction of an aggre
gate forward utility\, market consistent\,\nthat aggregates the marginal u
tility of the heterogeneous agents. This construction\nis based on the agg
regation of the pricing kernels of each investor. As an application\nwe an
alyze the impact of the heterogeneity and of the wealth market on the yiel
d curve.\n\nThis is a joint work with Nicole El Karoui and Mohamed Mrad.\n
\nhttps://indico.math.cnrs.fr/event/3123/contributions/3141/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the conditions on pricing functional and trading strategies in
insider trading model
DTSTART:20180830T092000Z
DTEND:20180830T095000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3142@indico.math.cnrs.fr
DESCRIPTION:Speakers: Albina Danilova (LSE)\, Umut Cetin (LSE)\n\nIn this
talk I will present some "folk" results in insider trading literature. In
particular\, I will discuss conditions on pricing functional that are nece
ssary for existence of equilibrium\, as well as the ones that are necessar
y for existence of *inconspicuous* equilibrium. I will prove that one can
restrict insider trading strategies to absolutely continuous ones.\n\nhttp
s://indico.math.cnrs.fr/event/3123/contributions/3142/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Continuous-Time Constrained Stochastic Linear-Quadratic Control wi
th Financial Applications
DTSTART:20180829T153000Z
DTEND:20180829T160000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3144@indico.math.cnrs.fr
DESCRIPTION:Speakers: Xun LI (HK PolyU)\, James Jianhui Huang (HK PolyU)\,
Ying HU (University of Rennes1)\n\nThis work studies a class of continuou
s-time scalar-state stochastic Linear-Quadratic (LQ) optimal control probl
em with the linear control constraints. Using the state separation theorem
induced from its special structure\, we derive the analytical solution fo
r this class of problem. The revealed optimal control policy is a piece-wi
se affine function of system state. This control policy can be computed ef
ficiently by solving two Riccati equations off-line. Under some mild condi
tions\, the stationary optimal control policy can be also achieved for thi
s class of problem with infinite horizon. This result can be applied to so
lve the constrained dynamic mean-variance portfolio selection problem. Exa
mples shed light on the solution procedure of implementing our method.\n\n
https://indico.math.cnrs.fr/event/3123/contributions/3144/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mixed Deterministic and Random Optimal Control of Linear Stochasti
c Systems with Quadratic Costs
DTSTART:20180829T124000Z
DTEND:20180829T132000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3146@indico.math.cnrs.fr
DESCRIPTION:Speakers: Shanjian Tang (Fudan University\, School of Mathemat
ical Science)\, Ying Hu (Université Rennes 1)\n\nWe consider the mixed op
timal control of a linear stochastic system with a quadratic cost function
al\, with two controllers---one can choose only deterministic time functio
ns\, called the deterministic controller\, while the other can choose adap
ted random processes\, called the random controller. The optimal control i
s shown to exist under suitable assumptions. The optimal control is chara
cterized via a system of fully coupled forward-backward stochastic differe
ntial equations (FBSDEs) of mean-field type. We solve the FBSDEs via solut
ions of two (but decoupled) Riccati equations\, and give the respective op
timal feedback law for both deterministic and random controllers\, using s
olutions of both Riccati equations. The optimal state satisfies a linear s
tochastic differential equation (SDE) of mean-field type. Both the singula
r and infinite time-horizonal cases are also addressed. \n\nThis is a join
t work with Ying HU\, Universite de Rennes 1.\n\nhttps://indico.math.cnrs.
fr/event/3123/contributions/3146/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stochastic Stefan-type Problems and Order Book Dynamics
DTSTART:20180828T092000Z
DTEND:20180828T095000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3145@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marvin Mueller (ETH Zurich)\n\nMoving boundary probl
ems allow to model macroscopic systems with phase transition at an inner b
oundary. Motivated by problems in economics and finance\, more explicitely
price-time continuous modelling of the limit order book\, we consider a s
tochastic and non-linear extension of the classical Stefan-problem in one
space dimension. More precisely\, the dynamics on buy and sell side in an
electronic financial markets are modeled by respective second order stocha
stic partial differential equations which are separated by an inner interf
ace: the mid-price. We discuss new results beyond existence theory\, such
as approximations of the solution.\n\nhttps://indico.math.cnrs.fr/event/31
23/contributions/3145/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nonparametric Bayesian volatility estimation
DTSTART:20180830T100000Z
DTEND:20180830T103000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3150@indico.math.cnrs.fr
DESCRIPTION:Speakers: Peter Spreij (Korteweg-de Vries Institute for Mathem
atics\, Universiteit van Amsterdam)\n\nGiven discrete time observations ov
er a fixed time interval\, we study a nonparametric Bayesian approach to e
stimation of the volatility coefficient of a stochastic differential equat
ion. We postulate a histogram-type prior on the volatility with piecewise
constant realisations on bins forming a partition of the time interval. Th
e values on the bins are assigned an inverse Gamma Markov chain (IGMC) pr
ior. Posterior inference is straightforward to implement via Gibbs samplin
g\, as the full conditional distributions are available explicitly and tur
n out to be inverse Gamma. We also discuss in detail the hyperparameter se
lection for our method. Our nonparametric Bayesian approach leads to good
practical results in representative simulation examples. Finally\, we appl
y it on a classical data set in change-point analysis: weekly closings of
the Dow-Jones industrial averages. [Joint work with Shota Gugushvili\, Mor
itz Schauer and Frank van der Meulen.]\n\nhttps://indico.math.cnrs.fr/even
t/3123/contributions/3150/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stochastic control under periodic observation times
DTSTART:20180831T085000Z
DTEND:20180831T092000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3148@indico.math.cnrs.fr
DESCRIPTION:Speakers: Kazutoshi Yamazaki (Kansai University)\n\nWe conside
r a version of the stochastic control problem\, in which control opportuni
ties arrive only at the jump times of an independent Poisson process. We c
onsider perpetual American options\, optimal dividend problems\, and inven
tory control problems\, driven by a spectrally one-sided Levy process. In
particular\, we show that barrier-type strategies are optimal under suita
ble conditions. The optimal strategies and value functions are concisely w
ritten in terms of the scale functions. This talk is based on the joint wo
rk with A. Bensoussan and J.L. Perez.\n\nhttps://indico.math.cnrs.fr/event
/3123/contributions/3148/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:BSDE formulation of combined regular and singular stochastic contr
ol problems
DTSTART:20180831T120000Z
DTEND:20180831T123000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3151@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ying Hu (University of Rennes 1)\n\nIn this talk\, w
e study a class of combined regular and singular stochastic control proble
ms that can be expressed as constrained BSDEs. In the Markovian case\, thi
s reduces to a characterization through a PDE with gradient constraint. Bu
t the BSDE formulation makes it possible to move beyond Markovian models a
nd consider path-dependent problems. We also provide an approximation of t
he original control problem with standard BSDEs that yield a characterizat
ion of approximately optimal values and controls.\nThis is a joint work wi
th Bruno Bouchard and Patrick Cheridito.\n\nhttps://indico.math.cnrs.fr/ev
ent/3123/contributions/3151/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Skorokhod embedding problem and single jump martingales: a con
nection via change of time
DTSTART:20180828T151000Z
DTEND:20180828T154000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3149@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexander Gushchin (Steklov Mathematical Institute)\
n\nLet $\\overline N_t = \\sup_{s\\leq t} N_s$ be a running maximum of a l
ocal martingale $N$. We assume that $N$ is max-continuous\, i.e. $\\overli
ne N$ is continuous. The Skorokhod embedding problem corresponds to a spec
ial case where $N$ is a Brownian motion stopped at a finite stopping time
$\\tau$. Consider the change of time generated by the running maximum:\n $
\n \\sigma_t:=\\inf\\\,\\{s\\colon \\overline N_s>t\\}.\n $\n Then the tim
e-changed process $M:=N\\circ\\sigma$ has a simple structure:\n $\n M_t=N_
{\\sigma_t}= t\\wedge W - V1_{\\{t\\geq W\\}}\,\n $\n where $W:=\\overline
N_\\infty$ and $V:=\\overline N_\\infty-N_\\infty$ ($V$ is correctly defi
ned on the set $\\{\\overline N_\\infty < \\infty\\}$). Besides\, $M_\\inf
ty=N_\\infty$ and $\\overline M_\\infty=\\overline N_\\infty$. This simple
observation explains how we can use single jump martingales $M$ of the ab
ove form to describe properties of $N$. For example\, $N$ is a closed supe
rmartingale if and only $M$ is a martingale and the negative part of $W-V$
is integrable. Another example shows how to connect the Dubins-Gilat cons
truction of a martingale whose supremum is given by the Hardy-Littlewood m
aximal function and the Azéma-Yor construction in the Skorokhod embedding
problem.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3149/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Esscher pricing under progressive enlargement of information
DTSTART:20180829T074000Z
DTEND:20180829T082000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3152@indico.math.cnrs.fr
DESCRIPTION:Speakers: Tahir Choulli (UNiversity of Alberta)\n\nWe investig
ate the Esscher pricing rule and the Esscher prices\, when the ``public" f
low information denoted by $\\mathbb F$ is progressively enlarged by a ran
dom time $\\tau$\, for both discrete-time and continuous-time settings. $\
\tau$ can represent the death time of an agent\, default time of a firm\,
or more generally the occurrence time of an even that might impact the mar
ket somehow. Thus\, by considering the new flow of information $\\mathbb G
$ resulting from the expansion of the flow $\\mathbb F$ with $\\tau$\, we
address the stopped model $(S^{\\tau}$\,$\\mathbb{G})$ in different direc
tions and various frameworks. In discrete time\, for instance\, we describ
e the Esscher martingale measure for the general case in different manners
\, and we illustrate the results on particular cases of models for the pai
r $(S\,\\tau)$. To well illustrate the impact of $\\tau$ on the Esscher p
ricing rules and/or prices\, we consider the Black-Scholes model for $S$ a
nd a class of models for $\\tau$. For these models\, we describe the Essch
er martingale measures\, the Esscher prices for some death-linked contract
s\, the Greeks of these obtained Esscher prices\, and we compare the Essch
er prices with the Black-Scholes pricing formula. This talk is based on jo
int work with Haya Alsemary (University of Alberta).\n\nhttps://indico.mat
h.cnrs.fr/event/3123/contributions/3152/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exact spectral asymptotics of fractional processes with applicatio
ns to inference
DTSTART:20180828T095000Z
DTEND:20180828T102000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3155@indico.math.cnrs.fr
DESCRIPTION:Speakers: Pavel Chigansky (Université de Jerusalem)\, Dmytro
Marushkevych (Université du Maine)\, Marina Kleptsyna (Université du Mai
ne)\n\nMany problems of statistical inference can be solved\, using spectr
al decomposition\nof stochastic processes. The principal difficulty with t
his approach is that eigenproblems\nare notoriously hard to solve in a rea
sonably explicit form. In this talk I will survey some\nrecent results on
the exact asymptotics in eigenproblems for fractional processes and\ndiscu
ss their applications to parameter estimation and filtering.\n\nhttps://in
dico.math.cnrs.fr/event/3123/contributions/3155/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Can old-age provision benefit from recent developments in quantita
tive finance?
DTSTART:20180830T085000Z
DTEND:20180830T092000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3154@indico.math.cnrs.fr
DESCRIPTION:Speakers: Michael Schmutz (University of Berne)\n\nAmong other
factors\, the difficult market environment with its sustained low interes
t rates triggers certain adjustments of investment and product strategies
of life insurance companies and pension funds. In this context\, the role
of life insurance companies and pension funds as long-term investors has i
ncreasingly been discussed among the industry and financial market supervi
sory authorities. These discussions are often focused on the idea of tryin
g to benefit from the possibility of long-term hold to maturity strategies
partially based on assets providing a certain illiquidity premium. This i
dea is compared to alternative ideas regarding investment or resolution pl
ans for life insurance portfolios\, some of which are based on recent deve
lopments in quantitative finance. Furthermore\, the link between investmen
t plans and product design will also be briefly discussed.\n\nhttps://indi
co.math.cnrs.fr/event/3123/contributions/3154/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some existence and uniqueness results for obliquely reflected BSDE
s
DTSTART:20180831T123000Z
DTEND:20180831T130000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3156@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jean-François Chassagneux (Université Paris Didero
t)\, Adrien Richou (IMB - Université de Bordeaux)\n\nIn this talk\, we pr
esent some recent results on obliquely reflected BSDEs. In particular we a
re able to deal with assumptions on the generator weaker than in currently
known results. An existence and uniqueness result is obtained in a non Ma
rkovian framework by assuming some regularity on the terminal condition. M
oreover\, a general existence result is obtained in the Markovian framewor
k. We also present an application to some new optimal switching problems c
alled randomised switching problems.\nThis is a joint work with Jean-Fran
çois Chassagneux (University of Paris 7)\n\nhttps://indico.math.cnrs.fr/e
vent/3123/contributions/3156/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantile optimization under derivative constraint
DTSTART:20180831T151000Z
DTEND:20180831T154000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3174@indico.math.cnrs.fr
DESCRIPTION:Speakers: Zuoquan Xu (The Hong Kong Polytechnic University)\n\
nThis talk will focus on a new type of quantile optimization problems aris
ing\nfrom insurance contract design models. This type of optimization prob
lems is\ncharacterized by a constraint that the derivatives of the decisio
n quantile\nfunctions are bounded. Such a constraint essentially comes fro
m the\n“incentive compatibility” constraint for any optimal insurance
contract to\navoid the potential severe problem of moral hazard in insuran
ce contract\ndesign models. By a further development of the relaxation met
hod\, we\nprovide a systemic approach to solving this new type of quantile
optimization\nproblems. The optimal quantile is expressed via the solutio
n of a free\nboundary problem for a second-order nonlinear ordinary differ
ential equation\n(ODE)\, which is similar to the Black-Scholes ODE for per
petual American\noptions.\n\nhttps://indico.math.cnrs.fr/event/3123/contri
butions/3174/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linear-Quadratic-Gaussian Mixed Games with Input Constraint Involv
ing Major Agent and Heterogeneous Minor Agents
DTSTART:20180829T160000Z
DTEND:20180829T163000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3175@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jianhui Huang (Hong kong Polytechnic University)\n\n
We consider a class of linear-quadratic-Gaussian mean-field games with a m
ajor agent and considerable heterogeneous minor agents with mean-field int
eractions. The individual admissible controls are constrained in closed co
nvex subsets of the full space. The decentralized strategies for individua
l agents and the consistency condition system are represented in an unifie
d manner via a class of mean-field forward-backward stochastic differentia
l equation involving projection operators. The well-posedness of consisten
cy condition system is established and the related ε−Nash equilibrium p
roperty is also verified.\n\nhttps://indico.math.cnrs.fr/event/3123/contri
butions/3175/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Infinite dimensional polynomial processes
DTSTART:20180829T095000Z
DTEND:20180829T102000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3176@indico.math.cnrs.fr
DESCRIPTION:Speakers: Christa Cuchiero (University of Vienna)\n\nMotivated
from high and infinite dimensional problems in mathematical finance\, we
consider infinite dimensional polynomial processes taking values in certai
n space of measures or functions. We have two concrete applications in min
d: first\, modeling high or even potentially infinite dimensional financia
l markets in a tractable and robust way\, and second analyzing stochastic
Volterra processes\, which recently gained popularity through rough volati
lity models and ambit processes. The first question leads to probability m
easure valued polynomial diffusions and the second one to Markovian lifts
of polynomial Volterra processes. For both cases we provide existence resu
lts and a moment formula.\n\nhttps://indico.math.cnrs.fr/event/3123/contri
butions/3176/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Generalized Feller processes and Markovian lifts of stochastic Vol
terra processes: the affine case
DTSTART:20180831T070000Z
DTEND:20180831T074000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3177@indico.math.cnrs.fr
DESCRIPTION:Speakers: Josef Teichmann (ETH Zurich)\n\nWe consider stochast
ic (partial) differential equations appearing as Markovian lifts of affine
Volterra processes with jumps from the point of view of the generalized F
eller property which was introduced in\, e.g.\, Dörsek-Teichmann (2010).
In particular we provide new existence\, uniqueness and approximation resu
lts for Markovian lifts of affine rough volatility models of general jump
diffusion type. We demonstrate that in this Markovian light the theory of
stochastic Volterra processes becomes almost classical.\n\nhttps://indico.
math.cnrs.fr/event/3123/contributions/3177/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Neumann Boundary Problem for Elliptic Partial Differential Equ
ations with Nonlinear Divergence Terms
DTSTART:20180831T154000Z
DTEND:20180831T161000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3178@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jing Zhang (Fudan University)\n\nWe prove the existe
nce and uniqueness of weak solution of a Neumann boundary problem for an e
lliptic partial differential equation (PDE for short) with a singular div
ergence term which can only be understood in a weak sense. A probabilistic
approach is applied by studying the backward stochastic differential equa
tion (BSDE for short) corresponding to the PDE.\n\nhttps://indico.math.cnr
s.fr/event/3123/contributions/3178/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Double continuation regions for American and Swing options with ne
gative discount rate in Lévy models
DTSTART:20180831T074000Z
DTEND:20180831T082000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3179@indico.math.cnrs.fr
DESCRIPTION:Speakers: Zbigniew Palmowski (Wrocław University of Science a
nd Technology)\n\nIn this talk we\nanalyze perpetual American call and put
options in an exponential L\\'evy model. \nWe consider a negative effecti
ve discount rate which arises in a number of financial applications\ninclu
ding stock loans and real options\, where the strike price can potentially
grow at a higher rate than\nthe original discount factor. We show that in
this case a double continuation region arises and we identify the two cri
tical prices. \nWe also generalize this result to multiple stopping proble
ms of swing type\, that is\, when\nsuccessive exercise opportunities are s
eparated by i.i.d. random\nrefraction times. We conduct numerical analysis
for the Black-Scholes model and\nthe jump-diffusion model with exponentia
lly distributed jumps.\n\nhttps://indico.math.cnrs.fr/event/3123/contribut
ions/3179/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3179/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duality for homogeneous optimisation problems
DTSTART:20180829T145000Z
DTEND:20180829T152000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3180@indico.math.cnrs.fr
DESCRIPTION:Speakers: Michael Tehranchi (University of Cambridge)\n\nThis
talk is concerned with stochastic optimal control problems with a certain
homogeneity. For such problems\, a novel dual problem is formulated. The r
esults are applied to a stochastic volatility variant of the classical Mer
ton problem. Another application of this duality is to the study the right
-most particle of a branching Levy process.\n\nhttps://indico.math.cnrs.fr
/event/3123/contributions/3180/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3180/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The asymptotic expansion of the regular discretization error of It
ô integrals
DTSTART:20180828T085000Z
DTEND:20180828T092000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3181@indico.math.cnrs.fr
DESCRIPTION:Speakers: Masaaki Fukasawa (Osaka University)\n\nWe study a Ed
geworth-type refinement of the central limit theorem for the discretizacio
n error of Itô integrals. Towards this end\, we introduce a new approach\
, based on the anticipating I Itô formula. This alternative technique all
ows us to compute explicitly the terms of the corresponding expansion form
ula. A joint work with E. Alos.\n\nhttps://indico.math.cnrs.fr/event/3123/
contributions/3181/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3181/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Representation of limit values for nonexpansive stochastic differe
ntial games
DTSTART:20180831T143000Z
DTEND:20180831T150000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3182@indico.math.cnrs.fr
DESCRIPTION:Speakers: Juan Li (Shandong University\, Weihai)\n\nA classica
l problem in ergodic control theory consists in the study of the limit beh
aviour of\nλV λ (·) as λ ↘ 0\, when V λ is the value function of a
deterministic or stochastic control problem\nwith discounted cost function
al with infinite time horizon and discount factor λ. We study this\nprobl
em for the lower value function V λ of a stochastic differential game wit
h recursive cost\, i.e.\,\nthe cost functional is defined through a backwa
rd stochastic differential equation with infinite\ntime horizon. But unlik
e the ergodic control approach\, we are interested in the case where the\n
limit can be a function depending on the initial condition. For this we ex
tend the so-called\nnon-expansivity assumption from the case of control pr
oblems to that of stochastic differential\ngames.\nBased on a joint work w
ith Rainer Buckdahn (Brest\, France)\, Nana Zhao (Weihai\, China).\n\nhttp
s://indico.math.cnrs.fr/event/3123/contributions/3182/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3182/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the geometry of very rough Weierstrass curves: local time\, SBR
measure\, Hausdorff dimension
DTSTART:20180830T071000Z
DTEND:20180830T075000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3185@indico.math.cnrs.fr
DESCRIPTION:Speakers: Peter Imkeller (Mathematisches Institut der Humboldt
-Universität zu Berlin)\n\nWe investigate geometric properties of Weierst
rass curves with two\ncomponents\, representing series based on trigonomet
ric functions. They\nare seen to be 12 − Hölder continuous\, and are no
t (para-)controlled\nwith respect to each other in the sense of the recent
ly established\nFourier analytic approach of rough path analysis. Their gr
aph is rep-\nresented as an attractor of a smooth random dynamical system.
For\none-dimensional versions we show existence of a local time and smoot
h-\nness of the Sinai-Bowen-Ruelle (SBR) measure. Our argument that its\ng
raph has Hausdorff dimension 2 is in the spirit of Ledrappier-Young’s\na
pproach of the Hausdorff dimension of attractors. This is joint work\nwith
G. dos Reis (U Edinburgh) and A. Réveillac (U Toulouse).\n\nhttps://indi
co.math.cnrs.fr/event/3123/contributions/3185/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3185/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On multisided optimal stopping problems for Levy processes
DTSTART:20180829T092000Z
DTEND:20180829T095000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3188@indico.math.cnrs.fr
DESCRIPTION:Speakers: Elena Boguslavskaya (Brunel University London)\n\nIn
the last decades solving multisided optimal stopping problems was of inte
rest.\n\nWe will show how to approach the above problems for Levy processe
s if the payoff function is an exponential polynomial (possibly multidimen
sional)\, and present several examples. The method we use is based on Appe
ll integral transform.\n\nhttps://indico.math.cnrs.fr/event/3123/contribut
ions/3188/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Entropie Minimal Martingale Measure for Lévy Processes
DTSTART:20180831T092000Z
DTEND:20180831T095000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3189@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hans-Jürgen Engelbert (Friedrich Schiller-Universit
y of Jena\, Institute of Mathematics)\n\nWe consider a geometric Lévy mar
ket with asset price S t = S 0 exp(X t )\, where X is a\ngeneral Lévy pro
cess on (Ω\, F\, P)\, and interest rate equal to zero. As it is well know
n\,\nexcept for the cases that X is a Brownian motion or a Poisson process
\, the market is\nincomplete. Therefore\, if the market is arbitrage-free\
, there are many equivalent mar-\ntingale measures and the problem arises
to choose an appropriate martingale measure\nfor pricing contingent claime
s.\nOne way is to choose the equivalent martingale measure Q ∗ which min
imizes the\nrelative entropie to P\, if it exists. Another choice is the f
amous Esscher martingale\nmeasure Q E \, if it exists.\nThe main objective
of the present talk is to discuss a simple and rigorous approach\nfor pro
ving the fact that the entropie minimal martingale measure Q ∗ and the E
sscher\nmartingale measure Q E actually coincide: Q ∗ = Q E . Our method
consists of a suit-\nable approximation of the physical probability measu
re P by Lévy preserving probaility\nmeasures P n.\nThe problem was treate
d in several earlier papers but more heuristally or in a so-\nphisticated
way.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3189/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Optimal (financial) position targeting via decoupling fields
DTSTART:20180831T130000Z
DTEND:20180831T133000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3147@indico.math.cnrs.fr
DESCRIPTION:Speakers: Stefan Ankirchner (University of Jena)\n\nIn the tal
k we consider a variant of the basic problem of the calculus of variations
\, where the Lagrangian is convex and subject to randomness adapted to a B
rownian filtration. We solve the problem by reducing it\, via a limiting a
rgument\, to an unconstrained control problem that consists in finding an
absolutely continuous process minimizing the expected sum of the Lagrangia
n and the deviation of the terminal state from a given target position. Us
ing the Pontryagin maximum principle one can characterize a solution of th
e unconstrained control problem in terms of a fully coupled forward-backwa
rd stochastic differential equation (FBSDE). We use the method of decoupli
ng fields for proving that the FBSDE has a unique solution.\nThe talk is b
ased on joint work with Alexander Fromm\, Thomas Kruse and Alexandre Popie
r.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3147/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On sets of laws of continuous martingales
DTSTART:20180828T154000Z
DTEND:20180828T161000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3191@indico.math.cnrs.fr
DESCRIPTION:Speakers: Youri Kabanov (Lomonosov Moscow State University and
Université de Bourgogne Franche-Comté)\n\nWe discuss relations between
sets of laws of stochastic integrals with respect to a Wiener process \nan
d general continuous martingales having quadratic characteristics whose RN
-derivatives evolve in the \nsame convex set of positive semidefinite symm
etric matrices.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/31
91/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Couplings on Wiener space and a new version of Talagrand’s inequ
ality
DTSTART:20180828T074000Z
DTEND:20180828T082000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3186@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hans Foellmer (Humboldt University Berlin)\n\nWe dis
cuss adaptive and anticipating couplings on Wiener space. In particular we
take a fresh look at the connection between the Wasserstein metric and th
e relative entropy with respect to Wiener measure provided by Talagrand’
s inequality and its extension to Wiener space by Feyel and Ustunel. Using
results of Nina Gantert for large deviations in the quadratic variation o
f Brownian motion\, we extend this inequality beyond the absolutely contin
uous case\, using the notion of specific relative entropy.\n\nhttps://indi
co.math.cnrs.fr/event/3123/contributions/3186/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3186/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Solution to the Time-Scale Fractional Puzzle in the Implied Vola
tility
DTSTART:20180829T070000Z
DTEND:20180829T074000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3192@indico.math.cnrs.fr
DESCRIPTION:Speakers: Masaaki Kijima (Tokyo Metropolitan University)\n\nIn
the option pricing literature\, it is well known that (i) the decrease in
the smile amplitude is much slower than the standard stochastic volatilit
y models and (ii) the term structure of the at-the-money volatility skew i
s approximated by a power-law function with the exponent close to zero. Th
ese stylized facts cannot be captured by standard models and\, while (i) h
as been explained by using a fractional volatility model with Hurst index
$H>1/2$\, (ii) is proved to be satisfied by a {\\it rough} volatility mode
l with $H<1/2$ under a risk-neutral measure. This paper provides a solutio
n to this fractional puzzle in the implied volatility. Namely\, we constru
ct a two-factor fractional volatility model and develop an approximation f
ormula for European option prices. It is shown through numerical examples
that our model can resolve the fractional puzzle\, when the correlations b
etween the underlying asset process and the factors of rough volatility an
d persistence belong to a certain range. More specifically\, depending on
the three correlation values\, the implied volatility surface is classifie
d into four types: (1) the roughness exists\, but the persistence does not
\; (2) the persistence exists\, but the roughness does not\; (3) both the
roughness and the persistence exist\; and (4) neither\nthe roughness nor t
he persistence exist. (Joint work with H. Funahashi)\n\nhttps://indico.mat
h.cnrs.fr/event/3123/contributions/3192/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Ruin Problem with Investment when the Risky Asset is a Semi
martingale
DTSTART:20180831T095000Z
DTEND:20180831T102000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3193@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jerome Spielmann (Universite d'Angers)\n\nIn this ta
lk\, we study the ruin problem with investment in a general framework wher
e the business part X is a Lévy process and the return on investment R is
a semimartingale. We obtain upper bounds on the finite and infinite time
ruin probabilities that decrease as a power function when the initial capi
tal increases. When R is a Lévy process\, we retrieve the well-known resu
lts. Then\, we show that these bounds are asymptotically optimal in the fi
nite time case\, under some simple conditions on the characteristics of X.
Finally\, we obtain a condition for ruin with probability one when X is a
Brownian motion with negative drift and express it explicitly using the c
haracteristics of R. (The results were obtained as a joint work with L. Vo
strikova.)\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3193/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3193/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Law of Large Numbers and Central Limit Theorem under Uncertainty o
f Probability Distributions
DTSTART:20180829T120000Z
DTEND:20180829T124000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3195@indico.math.cnrs.fr
DESCRIPTION:Speakers: Shige Peng (Shandong University)\n\nHow to calculate
the essential uncertainty of probability distributions hidden behind a re
al data sequence is a theoretically and practically important challenging
problem.\n\nRecently some fundamentally important progresses have been a
chieved in the domain of law of large numbers (LLN) and central limit the
orem (CLT) with a much weaker assumption of independence and identical dis
tribution (i.i.d.) under a sublinear expectation. \n\nThese new LLN and CT
L can be applied to a significantly wide classes of data sequence to cons
truct the corresponding optimal estimators. In particular\, many distribut
ion uncertainties hidden behind data sequences are able to be quantitativ
ely calculated by introducing a new algorithm of phi-max-mean type. \n\
nIn this talk\, I take some typical examples to provide a more concrete ex
planation of the above mentioned LLN and CLT\, the key idea of their proof
s\, as well as the new phi-max-mean estimators.\n\nhttps://indico.math.cn
rs.fr/event/3123/contributions/3195/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3195/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On discrete Schur-constant vectors\, with applications.
DTSTART:20180829T135000Z
DTEND:20180829T142000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3223@indico.math.cnrs.fr
DESCRIPTION:Speakers: Stéphane Loisel (Université de Lyon 1)\n\nThis tal
k is concerned with Schur-constant survival models for discrete random var
iables. Our main purpose is to prove that the associated partial sum proce
ss is a non- homogeneous Markov chain. This is shown in different cases a
s the random variables take values in the set of nonnegative integers or i
n the set of integers smaller than $m\\geq 1$. The property of Schur-const
ancy is also compared for thesecases. We also present a few additional res
ults on Schur-constant vectors. This is based on joint works with Castaner
\, Claramunt\, Lefèvre and Utev.\n\nhttps://indico.math.cnrs.fr/event/312
3/contributions/3223/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3223/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Utility maximization for Lévy switching models
DTSTART:20180828T143000Z
DTEND:20180828T150000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3224@indico.math.cnrs.fr
DESCRIPTION:Speakers: Yuchao Dong (University of Angers)\n\nThis article i
s devoted to the maximization of HARA utilities of Lévy\nswitching proces
s on finite time interval via dual method. We give the description\nof all
f-divergence minimal martingale measures in progressively enlarged\nfiltr
ation\, the expression of their Radon-Nikodym densities involving Hellinge
r\nand Kulback-Leibler processes\, the expressions of the optimal strategi
es for\nthe maximization of HARA utilities as well as the values of the co
rresponding\nmaximal expected utilities. The example of Brownian switching
models is presented.\n\nThis is common work with Lioudmila Vostrikova.\n\
nhttps://indico.math.cnrs.fr/event/3123/contributions/3224/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3224/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Controlled mean-field dynamics in stochastic control problems depe
nding on the law of state process
DTSTART:20180831T140000Z
DTEND:20180831T143000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3201@indico.math.cnrs.fr
DESCRIPTION:Speakers: Rainer Buckdahn (Université de Bretagne Occidentale
)\n\nThe starting point of the talk is a recent work with Juan Li (Shandon
g University\,\nWeihai\, P.R.China) and Jin Ma (University of South Califo
rnia\, Los Angeles\, U.S.A.)\, “A mean-\nfield stochastic control proble
m with partial observations” (Annals of Appl.Probability\, 2017: [1]) in
\nwhich we studied Pontryagin’s optimality principle for a stochastic co
ntrol problem whose dynamics\nare given by the stochastic differential equ
ation (SDE)\nZ t\nZ t\nX|Y\nX t = x +\nb(s\, X .∧s \, μ s \, u s (Y ))d
s +\nσ(s\, X .∧s \, μ s X|Y \, u s (Y ))dB s 1 \,\n0\n0\nR t\nY t = 0
h(s\, X s )ds + B t 2 \, t ∈ [0\, T ]\, P -a.s.\,\nwhere (B 1 \, B 2 ) i
s a P -Brownian motion\, the controlled state process X is only observable
through\nthe observation process Y and so the control process u = u(Y ) i
s a non anticipating functional of\nthe observation process Y . Moreover\,
unlike classical controlled dynamics\, the coefficients σ and b\ndo not
only depend on the paths of the controlled state process X and the control
u(Y ) but also\nX|Y\non the law μ s = P ◦ [E[X s |Y r \, r ≤ s]] −
1 \, s ∈ [0\, T ]. Motivations for such a type of dynamics are\ngiven in
[1]. However\, in [1] the dependence of the law is linear\; the talk will
study the case where\nthe coefficients are non linear functions of the la
w. Moreover\, unlike in [1] the coefficients b and σ\nare only supposed t
o be continuous in the law w.r.t. the 1-Wasserstein metric and on h we onl
y\nimpose boundedness and Lipschitz continuity in the state variable. The
main objective of the talk\nis to prove the weak existence and the uniquen
ess in law for the above dynamics.\n\nhttps://indico.math.cnrs.fr/event/31
23/contributions/3201/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lie group analysis of an optimization problem for a portfolio with
an illiquid asset
DTSTART:20180828T123000Z
DTEND:20180828T130000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3153@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ivan P. Yamshchikov (Max Planck Institute for Mathem
atics in the Sciences\, Leipzig\, Germany)\, Ljudmila A. Bordag (Universit
y of Applied Sciences Zittau/Gorlitz)\n\nWorking in the Merton's optimal c
onsumption framework with continuous time we consider an optimization pro
blem for a portfolio with an illiquid\, a risky and a risk-free asset. Our
goal in this paper is to carry out a complete Lie group analysis of PDEs
describing value function and investment and consumption strategies for a
portfolio with an illiquid asset that is sold in an exogenous random momen
t of time $T$ with a prescribed liquidation time distribution. The problem
of such type leads to three dimensional nonlinear Hamilton-Jacobi-Bellman
(HJB) equations. Such equations are not only tedious for analytical metho
ds but are also quite challenging form a numeric point of view. To reduce
the three-dimensional problem to a two-dimensional one or even to an ODE o
ne usually uses some substitutions\, yet the methods used to find such sub
stitutions are rarely discussed by the authors.\n\nWe use two types of uti
lity functions: general HARA type utility and logarithmic utility. We carr
y out the Lie group analysis of the both three dimensional PDEs and are ab
le to obtain the admitted symmetry algebras. Then we prove that the algebr
aic structure of the PDE with logarithmic utility can be seen as a limit o
f the algebraic structure of the PDE with HARA-utility as $\\gamma \\to 0$
. Moreover\, this relation does not depend on the form of the survival fun
ction $\\overline{\\Phi} (t)$ of the random liquidation time $T$.\nWe find
the admitted Lie algebra for a broad class of liquidation time distributi
ons in cases of HARA and log utility functions and formulate corresponding
theorems for all these cases.\n\nWe use found Lie algebras to obtain redu
ctions of the studied equations. Several of similar substitutions were use
d in other papers before whereas others are new to our knowledge. This met
hod gives us the possibility to provide a complete set of non-equivalent s
ubstitutions and reduced equations.\n\nWe also show that if and only if t
he liquidation time defined by a survival function $\\overline{\\Phi} (t)$
is distributed exponentially\, then for both types of the utility functi
ons we get an additional symmetry. We prove that both Lie algebras admit t
his extension\, i.e. we obtain the four dimensional $L^{HARA}_4$ and $L^{L
OG}_4$ correspondingly for the case of exponentially distributed liquidati
on time.\nWe list reduced equations and corresponding optimal policies tha
t tend to the classical Merton policies as illiquidity becomes small.\n\n
This research was supported by the European Union in the FP7-PEOPLE-2012-I
TN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action\, P
roject Multi-ITN STRIKE - Novel Methods in Computational Finance)\n\nhttps
://indico.math.cnrs.fr/event/3123/contributions/3153/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Recover Dynamic Utility from Monotonic Characteristic Processes
DTSTART:20180828T120000Z
DTEND:20180828T123000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3226@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nicole El Karoui\n\nIn the real world\, decision mak
ing under uncertainty is often viewed as an opti-\nmization problem under
choice criterium\, and most of theory focuses on the deriva-\ntion of the
"optimal decision" and its out-comes. But\, poor information is available\
non the criterium yielding to these observed data. The interesting problem
to infer\nthe unknown criterium from the known results is an example of i
nverse problem.\nHere we are concerned with a very simple version of the p
roblem: what does ob-\nservation of the "optimal" out-put tell us about th
e preference\, expressed in terms\nof expected utility\; in Economics\, th
is question was pioneered by the american\neconomist Samuelson in1938.\nTy
pically we try to reproduce the properties of the stochastic value functio
n of\na portfolio optimization problem in finance\, which satisfies the fi
rst order condi-\ntion U (t\, z)). In particular\, the utility process U i
s a strictly concave stochastic\nfamily\, parametrized by a number z ∈ R
+ (z 7→ U (t\, z))\, and the characteris-\ntic process X c = (X t c (x)
) is a non negative monotonic process with respect to\nits initial conditi
on x\, satisfying the martingale condition U (t\, X t c (x)) is a martin-\
ngale\, with initial condition U (0\, x) = u(x). We first introduce the ad
joint process\nY t (u x (x)) = U x (t\, X t c (x)) which is a characterist
ic process for the Fenchel transform\nof U if and only if X t c (x)Y t (u
x (x)) is a martingale. The minimal property is the\nmartingale property o
f Y t (u x (x)) with the x-derivative of X t c (x)\, which is sufficient\n
to reconstruct U from U x (t\, x) = Y t (u x ((X t c ) −1 (x))). Obvious
ly\, in general\, with-\nout additional constraints\, the characterization
is not unique. Various example are\ngiven\, in general motivated by finan
ce or economics: contraints on a characteristic\nportfolio in a economy at
the equilibrium\, thoptimal portfolio for a in complete\nfinancial market
\, under strongly orthogonality between X and Y \, the mixture of\ndiffere
nt economies....In any case\, the results hold for general but monotonic p
ro-\ncesses\, without semimartingale assumptions.\n\nhttps://indico.math.c
nrs.fr/event/3123/contributions/3226/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3226/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Decomposition of random times\, application to default times
DTSTART:20180828T130000Z
DTEND:20180828T133000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3183@indico.math.cnrs.fr
DESCRIPTION:Speakers: Monique Jeanblanc (université Evry Val d'ESSONNE)\,
Tahir Choulli\, Anna Aksamit\n\nWe provide a general model of default tim
e\, extending the models of Jiao and\nLi (modelling sovereign risks) and G
ehmlich and Schmidt (dynamic defaultable\nterm structure modelling beyond
intensity paradigm).\nWe show that any random time τ can be decomposed in
two parts as τ = τ 1 ∧τ 2\nunder the condition that the first random
time τ 1 avoids stopping times in the ref-\nerence filtration F\, and th
e second time τ 2 is thin\, i.e.\, its graph is included in a\ncountable
union of graphs of stopping times in the reference filtration F. Under the
\ncondition τ 1 ∨ τ 2 = ∞\, the decomposition is unique. This decomp
osition is based\non a study of the dual optional projection of τ \, as t
he decomposition of a stopping\ntime into accessible and totally inaccessi
ble is based on the dual predictable pro-\njection. We show that for a thi
n time τ 2 \, any F-martingale is a semimartingale in\nits progressive en
largement with τ 2 and we give its semimartingale decomposition.\nWe prov
e that any martingale in the reference filtration is a semimartingale in\n
the progressive enlargement with τ if and only if the same property holds
for the\nprogressive enlargement with τ 1 and we give its semimartingale
representation.\nWe establish in that the immersion property holds for τ
if and only if it holds\nfor τ 1 .This is a joint work with Anna Aksami
t and Tahir Choulli.\n\nhttps://indico.math.cnrs.fr/event/3123/contributio
ns/3183/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3183/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some sequential problems for Brownian motion with random drift in
statistics and finance.
DTSTART:20180828T070000Z
DTEND:20180828T074000Z
DTSTAMP:20230929T011100Z
UID:indico-contribution-3187@indico.math.cnrs.fr
DESCRIPTION:Speakers: Albert Shiryaev (Steklov Mathematical Institute)\n\n
We consider two models of observable process X = (X t ):\nModel A: X t =
μt + B t \,\nModel B: X t = μt + ν(t − θ)^+ + B t \,\nwhere B = (B t
) is a standard Brownian motion\, μ and ν are unknown parameters\,\nand
θ is a disorder time.\nFor Model A\, we consider some sequential statist
ical problems with different\nrisk functions.\nFor Model B\, we deal with
sequential problems of the following type:\nH 1 = sup EX τ\nor H 2 = sup
EE(X τ )\,\nτ ≤1\nτ ≤1\nwhere τ is a stopping time. We show that f
or such functionals H 1 and H 2 optimal\nstopping times have the following
form:\nτ ∗ = inf{t ≤ 1: ψ(t) ≥ a ∗ (t)}\,\nwhere ψ(t) is some
statistic of observations and a ∗ (t) is a curvilinear boundary\nsatisfy
ing the Fredholm integral equation of second order. These problems will\nb
e applied to the real asset price models (Apple\, Nasdaq).\nThe talk will
gives a survey of the joint papers of authors with Četin\,\nNovikov\, Zhi
tlukhin\, and Muravlev.\n\nhttps://indico.math.cnrs.fr/event/3123/contribu
tions/3187/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3187/
END:VEVENT
END:VCALENDAR